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researchv10 Dan Cross

.G1
frame ht 2.5 wid 2.5
coord x 0,1 y 0,1
label bot "Direction field is $y sup prime = x sup 2 / y$"
label left "$y = sqrt {(2x sup 3 +1)/3}$" right .3
ticks left in 0 at 0,1
ticks bot in 0 at 0,1
len = .04
for tx from .01 to .91 by .1 do {
	for ty from .01 to .91 by .1 do {
		deriv = tx*tx/ty
		scale = len/sqrt(1+deriv*deriv)
		line from tx,ty to tx+scale,ty+scale*deriv
	}
}
draw solid
for tx = 0 to 1 by .05 do {
	next at tx, sqrt((2*tx*tx*tx+1)/3)
}
.G2

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